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Pre-College MathClassifying Solids
PrismsPrisms are named for their base shape:
Rectangular PrismTriangular PrismHexagonal PrismPentagonal PrismOctagonal PrismTrapezoidal PrismSquare Prism
Prisms
Prisms are made up of two bases and rectangular faces connecting the edges of the bases two each other.
Cylinders
Cylinders have a circle for a base and one rectangular face curved around the circumference of the circle
Pyramids
Pyramids are named for their bases as wellRectangular PyramidTriangular PyramidHexagonal PyramidPentagonal PyramidOctagonal PyramidSquare Pyramid
Pyramids
Pyramids are made up of one base and triangles which converge at a point (vertex) opposite the base
Spheres and Hemispheres
Spheres are shaped like a round ball
A hemi-sphere is half a sphere
Cones
Cones have a circle for a base and a curved face that converges at a vertex opposite the base
HomeworkAssignment 10-6
Pre-College MathVolume of Prisms and Cylinders
What is volume?
The volume of a solid is the number of cubic units contained in its interior. Meaning how many cubic units it can “hold”.
The volume of an object is measured in cubic units (i.e. etc).
Volume of a Prism
The Volume of a Prism is found by taking the area of the base shape and multiplying it by the height if the prism
So the formula is: This works because you can think of
taking slices of the base shape and stacking them on top of each other
Some extras… Volume of a cube:
The volume of a cube is the cube of the length of its side:
Congruence:If two polyhedra (solid bounded by polygons)
are congruent, then they have the same volume
Volume Addition:The volume of a solid is the sum of the
volumes of all its NON-OVERLAPPING parts.
Helpful Hints
Area of a regular polygon:
Area of a rectangle:
Area of a triangle:
Volume of a Cylinder
This is the same as the volume of a prism with one little difference, the base is ALWAYS a circle
Therefore, the formula is:
HomeworkAssignment 10-7
Pre-College MathVolume of a Pyramid, Cone, and Sphere
Volume of a Pyramid
The Volume of a Pyramid is given by the area of the base of the pyramid times the height of the pyramid all divided by three
Thus, the formula is:
Volume of A Cone
The volume of a cone is given by the area of the circular base multiplied by the height od the cone, the whole quantity dived by three
Thus, the formula is:
Volume of a Sphere
The volume of a sphere is given by four thirds times pi times the radius of the sphere cubed (raised to a power of three).
Thus, the formula is:
HomeworkAssignment 10-8
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